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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    <a name="line.17"></a>
<FONT color="green">018</FONT>    package org.apache.commons.math3.distribution;<a name="line.18"></a>
<FONT color="green">019</FONT>    <a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.exception.NotStrictlyPositiveException;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.exception.util.LocalizedFormats;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.random.RandomGenerator;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.random.Well19937c;<a name="line.24"></a>
<FONT color="green">025</FONT>    <a name="line.25"></a>
<FONT color="green">026</FONT>    /**<a name="line.26"></a>
<FONT color="green">027</FONT>     * Implementation of the Zipf distribution.<a name="line.27"></a>
<FONT color="green">028</FONT>     *<a name="line.28"></a>
<FONT color="green">029</FONT>     * @see &lt;a href="http://mathworld.wolfram.com/ZipfDistribution.html"&gt;Zipf distribution (MathWorld)&lt;/a&gt;<a name="line.29"></a>
<FONT color="green">030</FONT>     * @version $Id: ZipfDistribution.java 1416643 2012-12-03 19:37:14Z tn $<a name="line.30"></a>
<FONT color="green">031</FONT>     */<a name="line.31"></a>
<FONT color="green">032</FONT>    public class ZipfDistribution extends AbstractIntegerDistribution {<a name="line.32"></a>
<FONT color="green">033</FONT>        /** Serializable version identifier. */<a name="line.33"></a>
<FONT color="green">034</FONT>        private static final long serialVersionUID = -140627372283420404L;<a name="line.34"></a>
<FONT color="green">035</FONT>        /** Number of elements. */<a name="line.35"></a>
<FONT color="green">036</FONT>        private final int numberOfElements;<a name="line.36"></a>
<FONT color="green">037</FONT>        /** Exponent parameter of the distribution. */<a name="line.37"></a>
<FONT color="green">038</FONT>        private final double exponent;<a name="line.38"></a>
<FONT color="green">039</FONT>        /** Cached numerical mean */<a name="line.39"></a>
<FONT color="green">040</FONT>        private double numericalMean = Double.NaN;<a name="line.40"></a>
<FONT color="green">041</FONT>        /** Whether or not the numerical mean has been calculated */<a name="line.41"></a>
<FONT color="green">042</FONT>        private boolean numericalMeanIsCalculated = false;<a name="line.42"></a>
<FONT color="green">043</FONT>        /** Cached numerical variance */<a name="line.43"></a>
<FONT color="green">044</FONT>        private double numericalVariance = Double.NaN;<a name="line.44"></a>
<FONT color="green">045</FONT>        /** Whether or not the numerical variance has been calculated */<a name="line.45"></a>
<FONT color="green">046</FONT>        private boolean numericalVarianceIsCalculated = false;<a name="line.46"></a>
<FONT color="green">047</FONT>    <a name="line.47"></a>
<FONT color="green">048</FONT>        /**<a name="line.48"></a>
<FONT color="green">049</FONT>         * Create a new Zipf distribution with the given number of elements and<a name="line.49"></a>
<FONT color="green">050</FONT>         * exponent.<a name="line.50"></a>
<FONT color="green">051</FONT>         *<a name="line.51"></a>
<FONT color="green">052</FONT>         * @param numberOfElements Number of elements.<a name="line.52"></a>
<FONT color="green">053</FONT>         * @param exponent Exponent.<a name="line.53"></a>
<FONT color="green">054</FONT>         * @exception NotStrictlyPositiveException if {@code numberOfElements &lt;= 0}<a name="line.54"></a>
<FONT color="green">055</FONT>         * or {@code exponent &lt;= 0}.<a name="line.55"></a>
<FONT color="green">056</FONT>         */<a name="line.56"></a>
<FONT color="green">057</FONT>        public ZipfDistribution(final int numberOfElements, final double exponent) {<a name="line.57"></a>
<FONT color="green">058</FONT>            this(new Well19937c(), numberOfElements, exponent);<a name="line.58"></a>
<FONT color="green">059</FONT>        }<a name="line.59"></a>
<FONT color="green">060</FONT>    <a name="line.60"></a>
<FONT color="green">061</FONT>        /**<a name="line.61"></a>
<FONT color="green">062</FONT>         * Creates a Zipf distribution.<a name="line.62"></a>
<FONT color="green">063</FONT>         *<a name="line.63"></a>
<FONT color="green">064</FONT>         * @param rng Random number generator.<a name="line.64"></a>
<FONT color="green">065</FONT>         * @param numberOfElements Number of elements.<a name="line.65"></a>
<FONT color="green">066</FONT>         * @param exponent Exponent.<a name="line.66"></a>
<FONT color="green">067</FONT>         * @exception NotStrictlyPositiveException if {@code numberOfElements &lt;= 0}<a name="line.67"></a>
<FONT color="green">068</FONT>         * or {@code exponent &lt;= 0}.<a name="line.68"></a>
<FONT color="green">069</FONT>         * @since 3.1<a name="line.69"></a>
<FONT color="green">070</FONT>         */<a name="line.70"></a>
<FONT color="green">071</FONT>        public ZipfDistribution(RandomGenerator rng,<a name="line.71"></a>
<FONT color="green">072</FONT>                                int numberOfElements,<a name="line.72"></a>
<FONT color="green">073</FONT>                                double exponent)<a name="line.73"></a>
<FONT color="green">074</FONT>            throws NotStrictlyPositiveException {<a name="line.74"></a>
<FONT color="green">075</FONT>            super(rng);<a name="line.75"></a>
<FONT color="green">076</FONT>    <a name="line.76"></a>
<FONT color="green">077</FONT>            if (numberOfElements &lt;= 0) {<a name="line.77"></a>
<FONT color="green">078</FONT>                throw new NotStrictlyPositiveException(LocalizedFormats.DIMENSION,<a name="line.78"></a>
<FONT color="green">079</FONT>                                                       numberOfElements);<a name="line.79"></a>
<FONT color="green">080</FONT>            }<a name="line.80"></a>
<FONT color="green">081</FONT>            if (exponent &lt;= 0) {<a name="line.81"></a>
<FONT color="green">082</FONT>                throw new NotStrictlyPositiveException(LocalizedFormats.EXPONENT,<a name="line.82"></a>
<FONT color="green">083</FONT>                                                       exponent);<a name="line.83"></a>
<FONT color="green">084</FONT>            }<a name="line.84"></a>
<FONT color="green">085</FONT>    <a name="line.85"></a>
<FONT color="green">086</FONT>            this.numberOfElements = numberOfElements;<a name="line.86"></a>
<FONT color="green">087</FONT>            this.exponent = exponent;<a name="line.87"></a>
<FONT color="green">088</FONT>        }<a name="line.88"></a>
<FONT color="green">089</FONT>    <a name="line.89"></a>
<FONT color="green">090</FONT>        /**<a name="line.90"></a>
<FONT color="green">091</FONT>         * Get the number of elements (e.g. corpus size) for the distribution.<a name="line.91"></a>
<FONT color="green">092</FONT>         *<a name="line.92"></a>
<FONT color="green">093</FONT>         * @return the number of elements<a name="line.93"></a>
<FONT color="green">094</FONT>         */<a name="line.94"></a>
<FONT color="green">095</FONT>        public int getNumberOfElements() {<a name="line.95"></a>
<FONT color="green">096</FONT>            return numberOfElements;<a name="line.96"></a>
<FONT color="green">097</FONT>        }<a name="line.97"></a>
<FONT color="green">098</FONT>    <a name="line.98"></a>
<FONT color="green">099</FONT>        /**<a name="line.99"></a>
<FONT color="green">100</FONT>         * Get the exponent characterizing the distribution.<a name="line.100"></a>
<FONT color="green">101</FONT>         *<a name="line.101"></a>
<FONT color="green">102</FONT>         * @return the exponent<a name="line.102"></a>
<FONT color="green">103</FONT>         */<a name="line.103"></a>
<FONT color="green">104</FONT>        public double getExponent() {<a name="line.104"></a>
<FONT color="green">105</FONT>            return exponent;<a name="line.105"></a>
<FONT color="green">106</FONT>        }<a name="line.106"></a>
<FONT color="green">107</FONT>    <a name="line.107"></a>
<FONT color="green">108</FONT>        /** {@inheritDoc} */<a name="line.108"></a>
<FONT color="green">109</FONT>        public double probability(final int x) {<a name="line.109"></a>
<FONT color="green">110</FONT>            if (x &lt;= 0 || x &gt; numberOfElements) {<a name="line.110"></a>
<FONT color="green">111</FONT>                return 0.0;<a name="line.111"></a>
<FONT color="green">112</FONT>            }<a name="line.112"></a>
<FONT color="green">113</FONT>    <a name="line.113"></a>
<FONT color="green">114</FONT>            return (1.0 / FastMath.pow(x, exponent)) / generalizedHarmonic(numberOfElements, exponent);<a name="line.114"></a>
<FONT color="green">115</FONT>        }<a name="line.115"></a>
<FONT color="green">116</FONT>    <a name="line.116"></a>
<FONT color="green">117</FONT>        /** {@inheritDoc} */<a name="line.117"></a>
<FONT color="green">118</FONT>        public double cumulativeProbability(final int x) {<a name="line.118"></a>
<FONT color="green">119</FONT>            if (x &lt;= 0) {<a name="line.119"></a>
<FONT color="green">120</FONT>                return 0.0;<a name="line.120"></a>
<FONT color="green">121</FONT>            } else if (x &gt;= numberOfElements) {<a name="line.121"></a>
<FONT color="green">122</FONT>                return 1.0;<a name="line.122"></a>
<FONT color="green">123</FONT>            }<a name="line.123"></a>
<FONT color="green">124</FONT>    <a name="line.124"></a>
<FONT color="green">125</FONT>            return generalizedHarmonic(x, exponent) / generalizedHarmonic(numberOfElements, exponent);<a name="line.125"></a>
<FONT color="green">126</FONT>        }<a name="line.126"></a>
<FONT color="green">127</FONT>    <a name="line.127"></a>
<FONT color="green">128</FONT>        /**<a name="line.128"></a>
<FONT color="green">129</FONT>         * {@inheritDoc}<a name="line.129"></a>
<FONT color="green">130</FONT>         *<a name="line.130"></a>
<FONT color="green">131</FONT>         * For number of elements {@code N} and exponent {@code s}, the mean is<a name="line.131"></a>
<FONT color="green">132</FONT>         * {@code Hs1 / Hs}, where<a name="line.132"></a>
<FONT color="green">133</FONT>         * &lt;ul&gt;<a name="line.133"></a>
<FONT color="green">134</FONT>         *  &lt;li&gt;{@code Hs1 = generalizedHarmonic(N, s - 1)},&lt;/li&gt;<a name="line.134"></a>
<FONT color="green">135</FONT>         *  &lt;li&gt;{@code Hs = generalizedHarmonic(N, s)}.&lt;/li&gt;<a name="line.135"></a>
<FONT color="green">136</FONT>         * &lt;/ul&gt;<a name="line.136"></a>
<FONT color="green">137</FONT>         */<a name="line.137"></a>
<FONT color="green">138</FONT>        public double getNumericalMean() {<a name="line.138"></a>
<FONT color="green">139</FONT>            if (!numericalMeanIsCalculated) {<a name="line.139"></a>
<FONT color="green">140</FONT>                numericalMean = calculateNumericalMean();<a name="line.140"></a>
<FONT color="green">141</FONT>                numericalMeanIsCalculated = true;<a name="line.141"></a>
<FONT color="green">142</FONT>            }<a name="line.142"></a>
<FONT color="green">143</FONT>            return numericalMean;<a name="line.143"></a>
<FONT color="green">144</FONT>        }<a name="line.144"></a>
<FONT color="green">145</FONT>    <a name="line.145"></a>
<FONT color="green">146</FONT>        /**<a name="line.146"></a>
<FONT color="green">147</FONT>         * Used by {@link #getNumericalMean()}.<a name="line.147"></a>
<FONT color="green">148</FONT>         *<a name="line.148"></a>
<FONT color="green">149</FONT>         * @return the mean of this distribution<a name="line.149"></a>
<FONT color="green">150</FONT>         */<a name="line.150"></a>
<FONT color="green">151</FONT>        protected double calculateNumericalMean() {<a name="line.151"></a>
<FONT color="green">152</FONT>            final int N = getNumberOfElements();<a name="line.152"></a>
<FONT color="green">153</FONT>            final double s = getExponent();<a name="line.153"></a>
<FONT color="green">154</FONT>    <a name="line.154"></a>
<FONT color="green">155</FONT>            final double Hs1 = generalizedHarmonic(N, s - 1);<a name="line.155"></a>
<FONT color="green">156</FONT>            final double Hs = generalizedHarmonic(N, s);<a name="line.156"></a>
<FONT color="green">157</FONT>    <a name="line.157"></a>
<FONT color="green">158</FONT>            return Hs1 / Hs;<a name="line.158"></a>
<FONT color="green">159</FONT>        }<a name="line.159"></a>
<FONT color="green">160</FONT>    <a name="line.160"></a>
<FONT color="green">161</FONT>        /**<a name="line.161"></a>
<FONT color="green">162</FONT>         * {@inheritDoc}<a name="line.162"></a>
<FONT color="green">163</FONT>         *<a name="line.163"></a>
<FONT color="green">164</FONT>         * For number of elements {@code N} and exponent {@code s}, the mean is<a name="line.164"></a>
<FONT color="green">165</FONT>         * {@code (Hs2 / Hs) - (Hs1^2 / Hs^2)}, where<a name="line.165"></a>
<FONT color="green">166</FONT>         * &lt;ul&gt;<a name="line.166"></a>
<FONT color="green">167</FONT>         *  &lt;li&gt;{@code Hs2 = generalizedHarmonic(N, s - 2)},&lt;/li&gt;<a name="line.167"></a>
<FONT color="green">168</FONT>         *  &lt;li&gt;{@code Hs1 = generalizedHarmonic(N, s - 1)},&lt;/li&gt;<a name="line.168"></a>
<FONT color="green">169</FONT>         *  &lt;li&gt;{@code Hs = generalizedHarmonic(N, s)}.&lt;/li&gt;<a name="line.169"></a>
<FONT color="green">170</FONT>         * &lt;/ul&gt;<a name="line.170"></a>
<FONT color="green">171</FONT>         */<a name="line.171"></a>
<FONT color="green">172</FONT>        public double getNumericalVariance() {<a name="line.172"></a>
<FONT color="green">173</FONT>            if (!numericalVarianceIsCalculated) {<a name="line.173"></a>
<FONT color="green">174</FONT>                numericalVariance = calculateNumericalVariance();<a name="line.174"></a>
<FONT color="green">175</FONT>                numericalVarianceIsCalculated = true;<a name="line.175"></a>
<FONT color="green">176</FONT>            }<a name="line.176"></a>
<FONT color="green">177</FONT>            return numericalVariance;<a name="line.177"></a>
<FONT color="green">178</FONT>        }<a name="line.178"></a>
<FONT color="green">179</FONT>    <a name="line.179"></a>
<FONT color="green">180</FONT>        /**<a name="line.180"></a>
<FONT color="green">181</FONT>         * Used by {@link #getNumericalVariance()}.<a name="line.181"></a>
<FONT color="green">182</FONT>         *<a name="line.182"></a>
<FONT color="green">183</FONT>         * @return the variance of this distribution<a name="line.183"></a>
<FONT color="green">184</FONT>         */<a name="line.184"></a>
<FONT color="green">185</FONT>        protected double calculateNumericalVariance() {<a name="line.185"></a>
<FONT color="green">186</FONT>            final int N = getNumberOfElements();<a name="line.186"></a>
<FONT color="green">187</FONT>            final double s = getExponent();<a name="line.187"></a>
<FONT color="green">188</FONT>    <a name="line.188"></a>
<FONT color="green">189</FONT>            final double Hs2 = generalizedHarmonic(N, s - 2);<a name="line.189"></a>
<FONT color="green">190</FONT>            final double Hs1 = generalizedHarmonic(N, s - 1);<a name="line.190"></a>
<FONT color="green">191</FONT>            final double Hs = generalizedHarmonic(N, s);<a name="line.191"></a>
<FONT color="green">192</FONT>    <a name="line.192"></a>
<FONT color="green">193</FONT>            return (Hs2 / Hs) - ((Hs1 * Hs1) / (Hs * Hs));<a name="line.193"></a>
<FONT color="green">194</FONT>        }<a name="line.194"></a>
<FONT color="green">195</FONT>    <a name="line.195"></a>
<FONT color="green">196</FONT>        /**<a name="line.196"></a>
<FONT color="green">197</FONT>         * Calculates the Nth generalized harmonic number. See<a name="line.197"></a>
<FONT color="green">198</FONT>         * &lt;a href="http://mathworld.wolfram.com/HarmonicSeries.html"&gt;Harmonic<a name="line.198"></a>
<FONT color="green">199</FONT>         * Series&lt;/a&gt;.<a name="line.199"></a>
<FONT color="green">200</FONT>         *<a name="line.200"></a>
<FONT color="green">201</FONT>         * @param n Term in the series to calculate (must be larger than 1)<a name="line.201"></a>
<FONT color="green">202</FONT>         * @param m Exponent (special case {@code m = 1} is the harmonic series).<a name="line.202"></a>
<FONT color="green">203</FONT>         * @return the n&lt;sup&gt;th&lt;/sup&gt; generalized harmonic number.<a name="line.203"></a>
<FONT color="green">204</FONT>         */<a name="line.204"></a>
<FONT color="green">205</FONT>        private double generalizedHarmonic(final int n, final double m) {<a name="line.205"></a>
<FONT color="green">206</FONT>            double value = 0;<a name="line.206"></a>
<FONT color="green">207</FONT>            for (int k = n; k &gt; 0; --k) {<a name="line.207"></a>
<FONT color="green">208</FONT>                value += 1.0 / FastMath.pow(k, m);<a name="line.208"></a>
<FONT color="green">209</FONT>            }<a name="line.209"></a>
<FONT color="green">210</FONT>            return value;<a name="line.210"></a>
<FONT color="green">211</FONT>        }<a name="line.211"></a>
<FONT color="green">212</FONT>    <a name="line.212"></a>
<FONT color="green">213</FONT>        /**<a name="line.213"></a>
<FONT color="green">214</FONT>         * {@inheritDoc}<a name="line.214"></a>
<FONT color="green">215</FONT>         *<a name="line.215"></a>
<FONT color="green">216</FONT>         * The lower bound of the support is always 1 no matter the parameters.<a name="line.216"></a>
<FONT color="green">217</FONT>         *<a name="line.217"></a>
<FONT color="green">218</FONT>         * @return lower bound of the support (always 1)<a name="line.218"></a>
<FONT color="green">219</FONT>         */<a name="line.219"></a>
<FONT color="green">220</FONT>        public int getSupportLowerBound() {<a name="line.220"></a>
<FONT color="green">221</FONT>            return 1;<a name="line.221"></a>
<FONT color="green">222</FONT>        }<a name="line.222"></a>
<FONT color="green">223</FONT>    <a name="line.223"></a>
<FONT color="green">224</FONT>        /**<a name="line.224"></a>
<FONT color="green">225</FONT>         * {@inheritDoc}<a name="line.225"></a>
<FONT color="green">226</FONT>         *<a name="line.226"></a>
<FONT color="green">227</FONT>         * The upper bound of the support is the number of elements.<a name="line.227"></a>
<FONT color="green">228</FONT>         *<a name="line.228"></a>
<FONT color="green">229</FONT>         * @return upper bound of the support<a name="line.229"></a>
<FONT color="green">230</FONT>         */<a name="line.230"></a>
<FONT color="green">231</FONT>        public int getSupportUpperBound() {<a name="line.231"></a>
<FONT color="green">232</FONT>            return getNumberOfElements();<a name="line.232"></a>
<FONT color="green">233</FONT>        }<a name="line.233"></a>
<FONT color="green">234</FONT>    <a name="line.234"></a>
<FONT color="green">235</FONT>        /**<a name="line.235"></a>
<FONT color="green">236</FONT>         * {@inheritDoc}<a name="line.236"></a>
<FONT color="green">237</FONT>         *<a name="line.237"></a>
<FONT color="green">238</FONT>         * The support of this distribution is connected.<a name="line.238"></a>
<FONT color="green">239</FONT>         *<a name="line.239"></a>
<FONT color="green">240</FONT>         * @return {@code true}<a name="line.240"></a>
<FONT color="green">241</FONT>         */<a name="line.241"></a>
<FONT color="green">242</FONT>        public boolean isSupportConnected() {<a name="line.242"></a>
<FONT color="green">243</FONT>            return true;<a name="line.243"></a>
<FONT color="green">244</FONT>        }<a name="line.244"></a>
<FONT color="green">245</FONT>    }<a name="line.245"></a>
<FONT color="green">246</FONT>    <a name="line.246"></a>




























































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